Sturdiness does not necessarily equate to better sound proofing, or thermal insulation for that matter.
That's the pain, when one replaces good old fashioned walls one can hang things on for improved sound/thermal characteristic which effectively make the wall unfit for purpose as far as putting anything on it is concerned. I only realised this when I put up coat pegs in the extended hall at my existing house. They all fell out because the thermo-type-block garbage couldn't hold them. It's a scandal ! an utter disgrace ! I ended up putting one back (all I really need) by drilling out a large diameter hole and plugging it with a decent filler, and then drilling again for the wall plug. Having created the problem in the first place, the industry is happy to charge you the earth for special wall plugs that can be screwed (?!?) into the wall, which, if you're lucky, and should hold fast.
In your case I think you need to go check what the wall between you and your neighbour really consists of. If it is the same rubbish they used in my extension then you can go to the DIY shed and buy those expensive thermal block fixings. Best of luck trying to screw them in without distorting or breaking them, or having the screwdriver slip and mark the surface though.